Patients, clinicians, and policymakers often need valid information about the real-world effects of drugs and other exposures for which there have been pronounced time-trends in use. For example, the rapid growth in the use of rofecoxib in the early 2000s and of exogenous testosterone from 2000?2013 was accompanied by an urgent need for knowledge about the cardiovascular effects of those drugs. Randomized trials seldom enroll a sufficient number of subjects, or follow them long enough, to examine associations with rare outcomes. Therefore, non-randomized studies are needed, even though they are susceptible to unmeasured confounding and other forms of bias. To address these limitations of available epidemiologic designs, we recently introduced the trend-in-trend design: a novel, hybrid epidemiologic-ecologic research design that is applicable when there is a prominent trend in the use of the study exposure. Substantial additional development is needed to realize the full public health impact of the trend-in-trend research design. Areas in most need of development include: evaluation of a sequential analysis extension for real-time post-marketing safety surveillance; evaluation of machine learning to specify the trend-in-trend design?s underlying cumulative probability of exposure model; evaluation of dose-response relationships; and evaluation of treatment effect heterogeneity based on baseline patient characteristics. For each of these methodologic needs, we propose an approach for which we will: 1) assess its statistical properties, in particular large-sample validity through asymptotics and finite sample statistical power; 2) evaluate its performance in thorough simulation studies; and 3) proof-test the approach using the known association between rofecoxib-acute myocardial infarction in healthcare data. Finally, we will apply these developments to the unresolved and highly important question of the cardiovascular, cerebrovascular, and thromboembolic effects of exogenous testosterone in men. This study will have broad scientific, clinical, and public health impact by greatly extending the utility of a novel epidemiologic research design with demonstrated validity and is applicable to a broad range of exposures with a prominent trend in use. It will also evaluate the safety of exogenous testosterone, a question of tremendous clinical and public health importance. Examining the safety of prescription drugs is one enormously important application of this design that has the potential to benefit many millions of people. As the trend-in-trend design is also applicable to non-drug exposures that have a pronounced time-trend (e.g., medical procedures, lifestyle factors, environmental exposures, etc.), its potential impact on the population is even broader.